Abstract: The first light from a supernova SN emerges once the SN shock breaks out ofthe stellar surface. The first light, typically a UV or X-ray flash, isfollowed by a broken power-law decay of the luminosity generated by radiationthat leaks out of the expanding gas sphere. Motivated by recent detection ofemission from very early stages of several SNe, we revisit the theory of shockbreakout and the following emission. We derive analytic light curves, payingspecial attention to the photon-gas coupling and deviations from thermalequilibrium. We then consider the breakout from several SNe progenitors. Wefind that for more compact progenitors, white dwarfs, Wolf-Rayet stars WRsand possibly more energetic blue-supergiant explosions, the observed radiationis out of thermal equilibrium at the breakout, during the planar phase i.e.,before the expanding gas doubles its radius, and during the early sphericalphase. Therefore, during these phases we predict significantly highertemperatures than previous analysis that assumed equilibrium. When thermalequilibrium prevails, we find the location of the thermalization depth and itstemporal evolution. Our results are useful for interpretation of early SN lightcurves. Some examples are: i Red supergiant SNe have an early bright peak inoptical and UV flux, less than an hour after breakout. It is followed by aminimum at the end of the planar phase about 10 hr, before it peaks againonce the temperature drops to the observed frequency range. In contrast WRsshow only the latter peak in optical and UV. ii Bright X-ray flares areexpected from all core-collapse SNe types. iii The light curve and spectrumof the initial breakout pulse holds information on the explosion geometry andprogenitor wind opacity. Its spectrum in compact progenitors shows anon-thermal power-law.